Effects of Knot Tightness at the Molecular Level

Effects of knot tightness at the molecular level

Liang Zhanga,b, Jean-François Lemonnierb, Angela Acocellac, Matteo Calvaresic, Francesco Zerbettoc,1, and David A. Leigha,b,1

aSchool of Chemistry and Molecular Engineering, East China Normal University, 200062 Shanghai, China; bSchool of Chemistry, University of Manchester, M13 9PL Manchester, United Kingdom; and cDipartimento di Chimica “G. Ciamician”, Università di Bologna, 40126 Bologna, Italy

Edited by Michael L. Klein, Institute of Computational Molecular Science, Temple University, Philadelphia, PA 19122, and approved December 18, 2018 (received for review September 8, 2018)

Three 819 knots in closed-loop strands of different lengths (∼20, by analogy to that previously used to prepare 1 (29). Treatment of 23, and 26 nm) were used to experimentally assess the conse- the ligands with equimolar amounts of FeCl2, followed by ring- quences of knot tightness at the molecular level. Through the closing metathesis (30), gave the corresponding 819 knot com- 1 use of H NMR, diffusion-ordered spectroscopy (DOSY), circular plexes [Fe4Knot](PF6)8 (Knot = 1–3; Fig. 1) which were isolated dichroism (CD), collision-induced dissociation mass spectrometry and characterized by electrospray ionization mass spectrometry (CID-MS) and molecular dynamics (MD) simulations on the different- and 1H NMR spectroscopy (SI Appendix, Figs. S1–S8). The 1H sized knots, we find that the structure, dynamics, and reactivity of NMR spectra of the three knotted complexes are essentially su- the molecular chains are dramatically affected by the tightness of perimposable (SI Appendix, Figs. S14 and S15), other than the the knotting. The tautness of entanglement causes differences in alkyl region due to the differences in chain length, indicating that conformation, enhances the expression of topological chirality, metal coordination of the knotted ligands holds the three com- weakens covalent bonds, inhibits decomplexation events, and plexes in similar conformations. Subjecting the metallated knots to changes absorption properties. Understanding the effects of tight- a 1:1 MeCN/NaOHaq (1 M) solution at 80 °C, followed by size- ening nanoscale knots may usefully inform the design of knotted exclusion chromatography, afforded the corresponding demetal- and entangled molecular materials. lated knots 1–3 with different degrees of tightness (Fig. 1 and SI Appendix, Figs. S9–S12). The BCRs (11) of 1–3 are 24, 27, and 30, molecular knots | supramolecular chemistry | chemical topology respectively. The diffusion coefficients (D) values of the three knots were measured by diffusion-ordered spectroscopy experi- nots are found in some proteins (1), linear and circular DNA ments; the relative effective hydrated radius of the knots increases K(2), and polymers of sufficient length and flexibility (3). The by 8% from 1 to 2 and 16% from 2 to 3 in line with the 12.5% and strand entanglements affect molecular size (4), stability (5), and 25% increase in the length of the flexible regions, respectively (SI various mechanical properties (6–8), although much of the un- Appendix, Figs. S19–S21). The optimized reaction times used in 1 derstanding as to how and why remains unclear. To date the the demetallation process were 15 min for [Fe4 ](PF6)8 (resulting 1 2 2 influence of various structural traits, such as the number of knot in a 35% yield of ), 10 min for [Fe4 ](PF6)8 (43% yield of ), and 3 3 crossings (9), writhe (10), backbone crossing ratio (BCR) (11), less than 5 min for [Fe4 ](PF6)8 (65% yield of ). The differences and the global radius of curvature (12), on properties has mainly in reactivity (yield and reaction time) can be rationalized by loos- been studied by simulations (13–16) rather than experiment (17, ening of the knot giving the strand significantly greater flexibility, 18). Knot tightness (19–21) is a particularly easy-to-appreciate particularly after displacement of the first iron cation. This makes it characteristic, familiar from our everyday experience in the easier for hydroxyl ions to access the remaining iron centers (31), macroscopic world, that may also have significant effects at the decreasing the amount of the poorly soluble iron bipyridine hy- molecular level (4, 22–27). Long polymers are predicted to have droxide by-products (32) that reduce the yield of metal-free knot. knotted regions that are both frequent and tight (25). The tightness of knotting is implicated in variations in the thermostability Significance of entangled proteins (26) and is thought to have consequences for tensile strength (27). However, it is difficult to assess intrinsic Knots and entanglements occur in proteins, DNA, and synthetic effects of knotting by comparing structures with rather different polymers and are being used to form the basis of interwoven chemical compositions. Monodispersed synthetic molecular knots nanomaterials. Understanding how the tautness of molecular are ideal models through which to evaluate the influence of knot entanglements affects properties is crucial for the future de- tightening on physical and chemical properties (17, 18). Here we sign of knotted, woven, and entangled molecules and mate- report experimentally determined property differences in a set of rials. However, while there are many theoretical studies on three knotted molecules that differ only in the length of flexible such systems there are very few experimental studies. Here we regions (alkyl chains) that separate more rigid sections (com- investigate the influence of knot tightness in a range of posed of aromatic rings) of the strand. Using a braiding strategy physical and chemical properties for three knots tied in 20-, 23-, previously used to assemble (28) an extremely tightly knotted and 26-nm closed-loop strands. We find that the tightness of 1 192-atom loop 819 knot ( ) (29), the alkene-terminated chains the molecular knots significantly affects reactivity, conforma- used to close the knotted structure were extended without tion, and the expression of chirality. otherwise altering the outcome of the knot synthesis (Fig. 1). This resulted in a set of three 819 molecular knots that differ Author contributions: L.Z., F.Z., and D.A.L. designed research; L.Z., J.-F.L., A.A., M.C., and only in the length of the alkyl chains in the loop (1 is 192 atoms F.Z. performed research; A.A., M.C., and F.Z. analyzed data; and L.Z., J.-F.L., A.A., M.C., long, 2 is 216 atoms long, and 3 is 240 atoms long, a 25% vari- F.Z., and D.A.L. wrote the paper. ation in strand length involving only the flexible regions). We The authors declare no conflict of interest. 1 probed the properties of the different-sized knots by HNMR This article is a PNAS Direct Submission. spectrometry, mass spectrometry, UV spectroscopy, and circu- Published under the PNAS license. lar dichroism, and used computational studies to help explain 1To whom correspondence may be addressed. Email: [email protected] or the role the increasing tightness of knotting plays in altering [email protected]. physical and chemical behavior. This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. Ligand strands L1–L3 bearing Tris(2,2′-bipyridine) motifs with 1073/pnas.1815570116/-/DCSupplemental. different lengths of alkene-terminated alkyl chains were prepared Published online January 25, 2019.

2452–2457 | PNAS | February 12, 2019 | vol. 116 | no. 7 www.pnas.org/cgi/doi/10.1073/pnas.1815570116 Downloaded by guest on September 23, 2021 CHEMISTRY

Fig. 1. Synthesis of [Fe4Knot](PF6)8 (Knot = 1–3) and their subsequent demetallation to 819 knots 1–3.

The yields of the demetallated 819 knots did not increase with The resonances of the aromatic protons in the looser knots, 2 longer reaction times. and 3, shift to low field, their chemical shifts moving closer to In contrast to the similar chemical environments observed for those of the corresponding building blocks (L2 and L3). The 1 1–3 the protons of the metallated knots, the H NMR spectra of shielding of Hd,He,Hf, and Hk, in particular, are intermediate differ markedly from each other in several regions (Fig. 2). between that of the corresponding protons in 1 and 3. Con- 1 Methylene (CH2)groupsHd and He in the tightest knot, , appear comitantly, the resonances of most of the alkyl protons (e.g., Hn) as multiplets because the constricted chiral environment accentu- move upfield. Both effects are consistent with a loss of π–π in- ates their diastereotopicity. With the loosening of the knot from 1 teractions in the tightly knotted structures and the rise of CH–π to 2,thesignalsofHd and He broaden, becoming a single broad interactions between the alkyl protons and aromatic motifs in the signal (at 600 MHz in CDCl3)in3 in line with the protons occu- looser knots (Fig. 2B and SI Appendix, Fig. S22 and Table S1). It pying less-constricted, less well-defined, environments (Fig. 2C). suggests that the conformation of the tightest knot, 1, is stabilized Variable-temperature 1H NMR spectra of 1–3 show little change by π–π stacking with the aromatic groups involved in the entangled over a large temperature range (238–318 K), indicating that the region of the structure with the alkyl chains to the outside. In variances in the 1H NMR spectra of the three knots are primarily 2 and 3, the longer alkyl chains slip into the knotted region due to the differences in tightness affecting conformation and not while the aromatic groups move to the periphery, thus gener- general dynamic phenomena (SI Appendix, Figs. S16–S18). ating fewer π–π interactions but more CH–π interactions. These

Zhang et al. PNAS | February 12, 2019 | vol. 116 | no. 7 | 2453 Downloaded by guest on September 23, 2021 1 Fig. 2. Partial H NMR spectra (600 MHz, CDCl3, 298 K) of 819 knots 1, 2, and 3;(A) region 0.25–10.0 ppm. (B) Expanded regions 8.3–8.8 ppm. (C) Expanded regions 4.1–4.7 ppm. Residual solvent peaks are shown in gray. The lettering corresponds to the proton labeling in Fig. 1.

observations provide experimental evidence in support of the [Fe41](PF6)7Cl (29), removing the iron cations and counter- migration of entanglements from rigid to flexible regions, be- anions, and increasing the chain length for 2 and 3. A summary of havior that has been predicted in simulations of knotted poly- the dynamics in terms of principal component analysis (PCA) mers (33, 34). maps is shown in Fig. 3 A–C. (For illustrative examples of pop- To help explain the experimental data, molecular-dynamics ulated conformations during the simulations, see SI Appendix, calculations were performed on 1–3. The starting geometries Figs. S32–S34.) The tightest knot 1 shows markedly different were based on the X-ray structure of the metallated knot dynamics with respect to knots 2 and 3 and is locked into

Fig. 3. Normalized free energy surfaces, according to PCA of (A) knot 1.(B) Knot 2 and (C) knot 3. The x and y axis are displacement vectors spread over the entire system, i.e., how much each atom “moves.” They are calculated with respect to an average structure (physically meaningless) and can be thought of

directions of flexibility. (D) TD-DFT (M06-2X/6–31G*) calculated four-dimensional plot of θ1 and θ2 together with the associated wavelength of excitation and the oscillator strength (in color scale of the phenyl-bipyridine fragment).

2454 | www.pnas.org/cgi/doi/10.1073/pnas.1815570116 Zhang et al. Downloaded by guest on September 23, 2021 + essentially a single conformation stabilized by strong π–π inter- were conducted on the [M + 2H]2 peak (Fig. 4 A, C, and E)of actions that involve every aromatic ring (Fig. 3A and SI Appen- knots 1–3 activated by collision-induced dissociation (CID). This dix, Fig. S32). The knot of intermediate tightness, 2, populates a resulted in multiply charged ions with a loss of mass consistent larger variety of conformations in which π–π interactions are with covalent bond scission and subsequent unraveling of the limited (Fig. 3B and SI Appendix, Fig. S33), while the loosest knotted strand (Fig. 4 B, D, and F). Upon increasing the nor- knot, 3, has no particularly preferred conformation (Fig. 3C and malized collision energy in 1-eV steps until bond cleavage oc- SI Appendix, Fig. S34). The Tris(2,2′-bipyridine) units, the most curred, the looser knots (2 and 3) required significantly higher rigid part of the structure, largely move out of the entangled energies (35 and 55 eV, respectively) to fragment than 1 (28 eV). region—and the alkyl chains, the more flexible region, move into For each knot scission always occurs at the carbon–oxygen bond it—in most of the thermally equilibrated conformations of the between the central bipyridine and phenyl–bipyridine units, but loosest knot, 3. This is consistent with the experimentally observed the knots showed two distinct types of fragmentation pattern 1H NMR shifts and illustrates how local flexibility of the strand (type I, Fig. 4G and type II, Fig. 4H). For the tightest knot 1, affects both conformation and the position of the entanglement. fragmentation (loss of a water molecule; m/z = 1,681.75) is The results of both experiment and simulation indicate that the followed by loss of an adjacent central bipyridine unit (m/z = B 3 dynamic properties of the 819 knots are profoundly influenced 1,582.67; Fig. 4 , type I). In contrast, the loosest knot re- by the tightness of the entanglements. quires a minimum of 55 eV to fragment and directly forms two To evaluate the effect of knot tightness on covalent bond breakdown products that each contain half of the knot (m/z = strengths, tandem mass spectrometry (MS-MS) experiments 2,008.36 and 1,810.45; Fig. 4F, type II). Both types of fragmentation CHEMISTRY

2+ Fig. 4. Fragmentation of 819 knots 1–3 under CID-MS experiments. (A) CID-MS of knot 1.(B) MS-MS of [M+2H] (m/z = 1,690.75) from knot 1, only type I fragmentation is observed. (C) CID-MS of knot 2.(D) MS-MS of [M+2H]2+ (m/z = 1859.00) from knot 2, both types of fragmentations are observed. (E) CID-MS + of knot 3.(F) MS-MS of [M + 2H]2 (m/z = 2,027.09) of knot 3, only type II fragmentation is observed. No fragment ions corresponding to macrocycles, which could arise from molecular links (e.g., a [2]catenane or Solomon link) upon fragmentation of one ring (17), was observed over a range of collision energies,

further demonstrating that only knots are present. (G and H) Two different fragmentation pathways (type I, G; type II, H)forthe819 knots corresponding to the MS-MS results shown in B, D, and E; bond cleavage is indicated with a red wavy line, the residues lost in the first step are colored purple, and those lost in the second step are colored blue.

Zhang et al. PNAS | February 12, 2019 | vol. 116 | no. 7 | 2455 Downloaded by guest on September 23, 2021 knots are highly sensitive to the two torsional angles, θ1 and θ2, within the phenyl–bipyridine moieties (Fig. 3D and SI Appendix, Figs. S35–S37). The observed red shift of knot 3 is due to the variation of θ1 and θ2 as the increased flexibility of the loose knot allows the chromophores to populate more conjugated, flatter, conformations. An 819 knot is intrinsically chiral by virtue of its topology. The enantiomers of 1–3 were isolated by chiral high-performance liquid chromatography (HPLC) and analyzed by CD spectroscopy (Fig. 5 and SI Appendix, Figs. S23 and S24). Each pair of knot enantiomers gives CD spectra of equal but opposite shape and sign (38, 39). As the knots become looser from 1 to 3, the change in the environment around the chromophores results in a red shift of the CD signal in the spectra of the respective molecules. The simulations and 1H NMR experiments suggest that the bipyridine and phenolic ethers are locked in a chiral conformation in the tightest knot, 1, which features strong π–π interactions. However, the looser knots have a variety of conformations that average out to give a weaker CD response. The red shift is a consequence of the more conjugated, flat, conformations of the chromophores in the looser knots. The dynamics and conformation of the knotted structures are clearly significantly affected by tightness, with the expression of chirality tunable by tightening or loosening the entanglement. Analysis of the molecular-dynamics simulations suggests that the property trends observed for 819 knots 1–3 are not a specific consequence of the particular aromatic-ring–based backbones of their structures. Atomic fluctuations measure the flexibility of (large) molecular systems. They are connected to the temperature B factor (40) that can be measured experimentally and is usually reported together with a protein structure in the Protein Data Bank. In the molecular-dynamics simulations, the size of Fig. 5. CD spectra of each enantiomer of molecular 819 knots 1, 2, and 3. the atomic fluctuations of the aromatic rings, the aliphatic chains, and the entire knot were found to be a function of tightness (Table 1): pattern are observed with knot 2 at 35 eV (Fig. 4D, m/z = 1,849.75 the tighter the knot, the smaller the fluctuations. The trends are and 1,750.83 for type I and m/z = 1,840.75 and 1,642.83 for type II). broadly similar for each of the three structural elements moni- Clearly knot tightness significantly affects covalent bond strength; tored (aromatics, aliphatics, and the whole molecule). the tighter the knot, the more easily some bonds can be broken. The structures of snapshots of the molecular dynamics that The experimental results are consistent with the simulations that successfully simulated the experimental data were used to in- suggest that tight knotting forces the adoption of conformations vestigate the interactions between the aromatic fragments and with strained bond lengths and angles. the strain energies of the alkyl chains in the three knots (Table Wiberg bond indices analysis, as implemented in the Gaussian09 1). The calculations were performed at the M06-2X/6-31G(d) suite of programs (35) was conducted with the Minnesota 2006 level of theory. For the interactions between aromatic rings, the hybrid meta exchange-correlation functional (M06-2X) (36) and correction for basis-set superposition error was determined using Pople’s basis set with polarization functions, 6-31G(d), on the the counterpoise method (41). In order of decreasing knot global minimum energy structures of doubly charged 1 and 3 to tightness (1 to 2 to 3), the average interaction energy between calculate the bond order of the carbon–oxygen bond between the aromatic fragments reduces from −48.3 to −40.1 to −23.6 kcal/mol central bipyridine and phenyl–bipyridine units (Ce–O–Cd, Fig. (Table 1). The variation reflects the greater strand dynamics 1). The calculations on the tightest knot, 1, show that one of as the knots become looser. In the same series the average these carbon–oxygen bonds is significantly weaker than others strain energies of the alkyl chains increase from 53.8, 160.0, and is more likely to break in the CID-MS experiments (SI and 260.1 kcal/mol, as more methylene groups are added to each Appendix, Fig. S38). After cleavage, the resulting terminal oxy- chain, forced by the knot topology to adopt strained dihedral gen atom can reorganize its electronic structure to allow loss of angles and CH–CH steric clashes. Aromatic stacking interactions a water molecule (Fig. 4G). In the loosest knot, 3, the carbon– do not generate favored conformations in the more flexible knots, oxygen bonds all have similar bond orders that are higher than but rather form to alleviate strain when the tightness of knotting the weak C–O bond in 1. This can result in near-simultaneous forces the molecule to become more compact. The stacking of cleavage of two C–O bonds at higher energy (SI Appendix, Fig. aromatic rings is a consequence of knot tightness rather than the S38), to produce the two halves of 3 observed experimentally (Fig. 4H). Δ 2 The effect of knot tightness on the spectral properties of 1–3 Table 1. Atomic fluctuations, (Å ), aromatic fragment was also investigated. The UV-vis spectra of knots 1 and 2 are interactions, Efrag (kcal/mol), and strain energy of the alkyl chain, Estrain (kcal/mol), of the three knots (1–3) similar, with a slight decrease in absorption at λmax = 306 nm for 2. However, the absorption of the loosest knot, 3, decreases Knot Δaromatic rings Δentire knot Δalkyl chain Efrag Estrain significantly and is associated with a 10-nm red shift (SI Appendix, 1 2.26 2.31 2.66 −48.3 53.8 Fig. S25). Simulated spectra, generated from time-dependent − density functional theoretical (37) calculations at the M06-2X/ 2 4.95 5.39 6.86 40.1 160.0 3 7.43 8.42 10.77 −23.6 260.1 6–31G(d) level of theory, show that the electronic spectra of the

2456 | www.pnas.org/cgi/doi/10.1073/pnas.1815570116 Zhang et al. Downloaded by guest on September 23, 2021 driving force behind its conformation/structure. The aromatic prove useful in understanding the role of knotting in entangled rings in the Tris(2,2′-bipyridine) ligand strands are necessary for polymers and in the design of future knotted and interwoven 1 the knot synthesis and, in some cases ( H NMR, CD spectra), nanomaterials (42–45). provide useful probes for the experimental detection of behavior. If π-stacking was the dominating interaction that determined Materials and Methods their conformation, the knots would not be the highly dynamic Synthesis. Molecular knots 2 and 3 were prepared by modifying the braiding systems that experiments and simulations show them to be. It strategy previously used (29) to assemble knot 1 (Fig. 1). Subjecting each

therefore seems likely that the trends observed for 1–3 are not metallated knot ([Fe41](PF6)7Cl, [Fe42](PF6)7Cl, or [Fe43](PF6)7Cl) to a 1:1

directly related to their particular molecular make-up but will MeCN/NaOHaq (1 M) solution at 80 °C, followed by size-exclusion chroma- more generally reflect aspects of behavior regarding knot tight- tography, afforded the corresponding demetallated knots 1–3, which were ness at the nanoscale. characterized by NMR and mass spectrometry. The enantiomers of 1–3 were isolated by chiral HPLC and analyzed by CD spectroscopy. Conclusions Molecular-Dynamics Simulations. Molecular-dynamics simulations were car- A series of molecular 819 knots that differ only in the length of alkyl chains that connect rigid aromatic regions enable the in- ried out with the AMBER 12.0 suite of programs. The knots were parame- vestigation of the influence of knot tightness on a range of trized using the general AMBER force field and the standard restrained physical and chemical properties, allowing experimental obser- electrostatic potential procedure carried out to assign charges to atoms by 8+ vations to be rationalized through computational simulations. Antechamber. The crystallographic structure of metallated knot [Fe41] was used as the starting structure for 1 and as a template for 2 and 3. The tightness of molecular 819 knots affects reactivity (the rate of demetallation of knotted ligands and collision energies required for bond breaking), conformation (rigid regions preferring to be ACKNOWLEDGMENTS. We thank the China 1000 Talents Plan, East China Normal University, the Engineering and Physical Sciences Research Council outside the region of entanglement in looser structures), and the 1 (EP/P027067/1) and the European Research Council, Advanced Grant 339019 expression of topological chirality (manifest in CD and H NMR for funding, and the University of Manchester for a President’s Doctoral spectra). These results provide some experimental evidence of Scholar Award (to L.Z.). D.A.L. is a China 1000 Talents “Topnotch Talent” the effects of tightening knots at the molecular level, which should Professor and Royal Society Research Professor.

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